Extension refers to studying material not usually in a standard mathematics course. Usually this material is at a more challenging level than the typical material at this age level. Often, particularly at younger levels, this may involve a separate extension class. The mathematical topics typically studied in secondary schools, and those explicitly stated in the curriculum and assessed in NCEA examinations are only a small subset of those that secondary students are capable of learning. Some suggestions for suitable topics are:
Euclidean geometry and Euclid's elements
Non-euclidean geometry
Basic logic
Matrices
Vectors
Set theory
Induction as a means of proof
Graph theory
Fractals
Counting in other base systems - in particular representing numbers in binary
Clock arithmetic
Coding using mathematics
Divisibility, prime numbers and prime factorisations
While many of these topics move into very advanced mathematics, their most fundamental concepts are easily accessible by high school students, and in particular the gifted. Selection from these topics could be completed by the teacher, or informed by students interests and particular strengths within mathematics. Extension could also draw on strengths and interests from other curriculum areas.
One problem when providing extension work not related to the curriculum or standard assessment is that grade-focused students may not see the benefit in partaking in these activities. While teachers may then turn to acceleration or enrichment, it is useful to demonstrate the value of these forms of mathematical knowledge, and how these forms of knowledge will increase the range of the students problem solving skills, which will be valuable in all types of mathematics.
Extension
Extension refers to studying material not usually in a standard mathematics course. Usually this material is at a more challenging level than the typical material at this age level. Often, particularly at younger levels, this may involve a separate extension class. The mathematical topics typically studied in secondary schools, and those explicitly stated in the curriculum and assessed in NCEA examinations are only a small subset of those that secondary students are capable of learning. Some suggestions for suitable topics are:
While many of these topics move into very advanced mathematics, their most fundamental concepts are easily accessible by high school students, and in particular the gifted. Selection from these topics could be completed by the teacher, or informed by students interests and particular strengths within mathematics. Extension could also draw on strengths and interests from other curriculum areas.
One problem when providing extension work not related to the curriculum or standard assessment is that grade-focused students may not see the benefit in partaking in these activities. While teachers may then turn to acceleration or enrichment, it is useful to demonstrate the value of these forms of mathematical knowledge, and how these forms of knowledge will increase the range of the students problem solving skills, which will be valuable in all types of mathematics.